311.

The number of 3 x 3 matrices with entries - 1 or + 1 is

• 2^-4

• 2⁵

• 2⁶

• 2⁹

The value of a for which the matrix A = $\left[\begin{array}{cc}\mathrm{a}& 2\\ 2& 4\end{array}\right]$ is singular :

• $\mathrm{a} \ne 1$

• a = 1

• a = 0

• a = - 1

If A = $\left[\begin{array}{cc}2& - 1\\ - 1& 2\end{array}\right]$ and I is the unit matrix of order two, then A² is equal to :

• 4A - 3I

• 3A - 4I

• A - I

• A + I

If A and B are two square matrices of the same order, then (A - B)² :

• A² - AB - BA + B²

• A² - 2AB + B²

• A² - 2BA + B²

• A² - B²

If $\mathrm{P} = \left[\begin{array}{ccc}\mathrm{i}& 0& - \mathrm{i}\\ 0& - \mathrm{i}& \mathrm{i}\\ - \mathrm{i}& \mathrm{i}& 0\end{array}\right] \mathrm{and} \mathrm{Q} = \left[\begin{array}{cc}- \mathrm{i}& \mathrm{i}\\ 0& 0\\ \mathrm{i}& - \mathrm{i}\end{array}\right]$, then PQ is equal to

• $\left[\begin{array}{cc}- 2& 2\\ 1& - 1\\ 1& - 1\end{array}\right]$

• $\left[\begin{array}{cc}2& - 2\\ - 1& 1\\ - 1& 1\end{array}\right]$

• $\left[\begin{array}{cc}2& - 2\\ - 1& 1\end{array}\right]$

• $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

For what value of $\mathrm{\lambda }$ the system of equations x + y + z = 6, x + 2y + 3z = 10, x + 2y + $\mathrm{\lambda }$z = 10 is consistent ?

• 1

• 2

• - 1

• 3

If a = 1 + 2 + 4 + ... to n terms, b = 1 + 3 + 9 + ... to n terms and c = 1 + 5 + 25 + ... to n terms, then

$\left|\begin{array}{ccc}\mathrm{a}& 2\mathrm{b}& 4\mathrm{c}\\ 2& 2& 2\\ 2^{\mathrm{n}}& 3^{\mathrm{n}}& 5^{\mathrm{n}}\end{array}\right|$ equals :

• (30)ⁿ

• (10)ⁿ

• 0

• 2ⁿ + 3ⁿ + 5ⁿ

The matrix $\left[\begin{array}{ccc}5& 10& 3\\ - 2& - 4& 6\\ - 1& - 2& \mathrm{b}\end{array}\right]$ is a singular matrix, if b is equal to :

• - 3

• 3

• 0

• for any value of b

For non-singular square matrices A, B and C of the same order, (AB^-1C)^-1 is equal to :

• A^-1BC^-1

• C^-1B^-1A^-1

• CBA^-1

• C^-1BA^-1

Let A = $\left[\begin{array}{cc}{\cos }^2\left(\mathrm{\theta }\right)& \sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\theta }\right)\\ \cos \left(\mathrm{\theta }\right)\sin \left(\mathrm{\theta }\right)& {\sin }^2\left(\mathrm{\theta }\right)\end{array}\right]$ and B = $\left[\begin{array}{cc}{\cos }^2\left(\mathrm{\varphi }\right)& \sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\varphi }\right)\\ \cos \left(\mathrm{\varphi }\right)\sin \left(\mathrm{\varphi }\right)& {\sin }^2\left(\mathrm{\varphi }\right)\end{array}\right]$, then AB = 0 if :

• $\mathrm{\theta } = \mathrm{n\varphi }, \mathrm{n} = 0, 1, 2, ...$

• $\mathrm{\theta } + \mathrm{\varphi } = \mathrm{n\pi }, \mathrm{n} = 0, 1, 2, ...$

• $\mathrm{\theta } = \mathrm{\varphi } + \left(2\mathrm{n} + 1\right)\frac{\mathrm{\pi }}{2}, \mathrm{n} = 0, 1, 2, ...$

• $\mathrm{\theta } = \mathrm{\varphi } + \mathrm{n}\frac{\mathrm{\pi }}{2}, \mathrm{n} = 0, 1, 2, ...$